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Mirrors > Home > ILE Home > Th. List > breq12 | Unicode version |
Description: Equality theorem for a binary relation. (Contributed by NM, 8-Feb-1996.) |
Ref | Expression |
---|---|
breq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1 3902 | . 2 | |
2 | breq2 3903 | . 2 | |
3 | 1, 2 | sylan9bb 457 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 class class class wbr 3899 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 |
This theorem is referenced by: breq12i 3908 breq12d 3912 breqan12d 3915 posng 4581 isopolem 5691 poxp 6097 rbropapd 6107 ecopover 6495 ecopoverg 6498 ltdcnq 7173 recexpr 7414 ltresr 7615 reapval 8305 ltxr 9517 xrltnr 9521 xrltnsym 9534 xrlttr 9536 xrltso 9537 xrlttri3 9538 xposdif 9620 exmidsbthrlem 13113 |
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